Flat taxes may sound dull, but right-wingers love them and Tory cabinet office minister Oliver Letwin has suggested that a future Conservative government could bring them one in on income "when the economy improves".

His remarks have caused a stir. Labour's shadow chief Treasury secretary Chris Leslie seized on them as proof of "what's on the real Tory agenda for a second term".

Here's what you need to know about the tax system beloved by right-wingers and loathed by lefties.

Why are flat taxes so controversial?

A flat tax system would hit every taxpayer with the same tax rate, regardless of how much they earn. This means that, if a flat income tax rate was introduced, the poor would have to pay more to fill the gap of the tax cut enjoyed by the better off.

How much more would the poor have to pay?

According to the Institute for Fiscal Studies, a flat-rate income tax would have to hit everyone at 31% in order to avoid being an overall cost to the Treasury that would have to be compensated for with more cuts or short-term borrowing. Such a flat tax could be achieved by merging income tax and national insurance, something Osborne has been looking at for years.

Such a rate would mark a "huge increase" for the 24 million people on lower and middle incomes who currently pay income tax at 20p, while those earning over £150,000-a-year, paying a 45p top rate of income tax, would enjoy a massive cut.

Why do people support flat taxes then?

Supporters argue that a flat tax would boost economic activity and the Treasury's tax take as the country attracts more foreign investment and businesses with its simple system, meaning they do not need an army of lawyers to navigate.

If it was not a "pure" flat tax system, middle-earners could pay the same rate as big-earners and enjoy a large slice of their income tax-free, enabling it to be in effect a progressive system.

George Osborne used to point to countries with flat taxes like Estonia as economies with "lessons we can learn from", but admitted that it was not very popular among "mature" economies. The Tory party has now gone cold on the idea, with a spokesman rejecting the idea "full stop".

Other Tory MPs are still great fans of flat taxes, like Jacob Rees-Mogg, who praised the idea as "very attractive".

Tory Edward Leigh told MPs: "If we had a flat tax rate of 22% with a £15,000 tax-free allowance, about 10 million of the poorest taxpayers would see their entire income tax burden disappear."